Accuracy too high too fast?
It actually depends on a couple of things here -


How many output classes do you have? If you have only 2 or 3 classes, it is a very easy task for the classifier that you have built. So, it is highly possible that convergence has occurred.
As @Djib2011 mentioned already, if your input training set is not balanced and is heavier with one of the output classes (95%), then this accuracy you see makes sense but note that your model won't do well in production.
Do not try to evaluate your model on the basis of your training accuracy. Test it on data your model has never seen before and then evaluate the classification accuracy making sure that your training/testing data is not heavy with one of the classes.